Large-scale Bose-Einstein condensation (BEC) of cesium atoms has been observed (T=343K). The technical bottleneck of BEC is very small trapping volume (10-8cm3), which made the number of condensed atoms still stagnant (less than 107), much smaller than normal condensation (more than 1013), large-scale BEC has never been observed. In BEC experiment, scientists have applied magnetic field (used to trap atoms) and laser (used to cool atoms), but never considered applying electric field, because they think that all kinds of atoms are non-polar atoms. The breakthrough of the bottleneck lies in the application of electric field. In theory, despite 6s and 6p states of cesium are not degenerate, but Cs may be polar atom doesn't conflict with quantum mechanics because it is hydrogen-like atom. When an electric field was applied, Cs atoms become dipoles, therefore large-scale BEC can be observed. BEC experiment of cesium has been redone. From the entropy S=0, critical voltage Vc=78V. When V < Vc, S > 0; when V > Vc, S<0, phase transition occurred. When V=370V, condensates contained up to 2.71×1017 atoms, a forty percent improvement over previous results. This BEC is a second-order phase transition because entropy doesn't show discontinuity, from Wikipedia. It is also equivalent to a quantum phase transition. The permanent dipole moment (PDM) of Cs atom has been accurately measured: dCs=[1.84±0.15(stat) ±0.11 (syst)] ×10-8 e.cm. The PDM doesn't arise from the nuclear spin but arises from asymmetrical charge distribution, and it doesn't violate both time reversal and parity symmetry. The maximum induced dipole moment is dind ≤ 2.12 ×10-13e.cm, which can be ignored. BEC has three main features: BEC is macroscopic occupation of the ground state of the system; BEC is condensation in momentum space; Bose gas would undergo a phase transition. Our experiment is an ideal BEC because it conforms to the three features. BEC belongs to the condensation of quantum gas, when V > Vc, almost all Cs atoms (bosons) are in exactly the same state，according to Feynman, “the quantum physics is the same thing as the classical physics”, so our classical theory can explain BEC experiment satisfactorily. Ultra-low temperature is to make Bose gas phase transition, we used critical voltage to achieve phase transition, ultra-low temperature is no longer necessary. Five innovative formulas were first reported in the history of physics, the publication of this article marking mankind will enter a new era of polar atoms.
Large-scale Bose-Einstein condensation (BEC) of cesium atoms has been observed (T=343K). The technical bottleneck of BEC is very small trapping volume (10-8cm3), which made the number of condensed atoms still stagnant (less than 107), much smaller than normal condensation (more than 1013), large-scale BEC has never been observed. In BEC experiment, scientists have applied magnetic field (used to trap atoms) and laser (used to cool atoms), but never considered applying electric field, because they think that all kinds of atoms are non-polar atoms. The breakthrough of the bottleneck lies in the application of electric field. In theory, despite 6s and 6p states of cesium are not degenerate, but Cs may be polar atom doesn't conflict with quantum mechanics because it is hydrogen-like atom. When an electric field was applied, Cs atoms become dipoles, therefore large-scale BEC can be observed. BEC experiment of cesium has been redone. From the entropy S=0, critical voltage Vc=78V. When V < Vc, S > 0; when V > Vc, S<0, phase transition occurred. When V=370V, condensates contained up to 2.71×1017 atoms, a forty percent improvement over previous results. This BEC is a second-order phase transition because entropy doesn't show discontinuity, from Wikipedia. It is also equivalent to a quantum phase transition. The permanent dipole moment (PDM) of Cs atom has been accurately measured: dCs=[1.84±0.15(stat) ±0.11 (syst)] ×10-8 e.cm. The PDM doesn't arise from the nuclear spin but arises from asymmetrical charge distribution, and it doesn't violate both time reversal and parity symmetry. The maximum induced dipole moment is dind ≤ 2.12 ×10-13e.cm, which can be ignored. BEC has three main features: BEC is macroscopic occupation of the ground state of the system; BEC is condensation in momentum space; Bose gas would undergo a phase transition. Our experiment is an ideal BEC because it conforms to the three features. BEC belongs to the condensation of quantum gas, when V > Vc, almost all Cs atoms (bosons) are in exactly the same state，according to Feynman, “the quantum physics is the same thing as the classical physics”, so our classical theory can explain BEC experiment satisfactorily. Ultra-low temperature is to make Bose gas phase transition, we used critical voltage to achieve phase transition, ultra-low temperature is no longer necessary. Five innovative formulas were first reported in the history of physics, the publication of this article marking mankind will enter a new era of polar atoms.
Large-scale BEC of cesium at T=353 K was first observed. Until now, scientists have applied magnetic fields and lasers, but never applied electric fields, and atoms are oriented at random, so observation of BEC is very difficult. Our innovation lies in the application of electric fields. We theoretically proved that alkali atom (include Cs) may be polar atom doesn't conflict with quantum mechanics. Variation of the capacitance with temperature offers a means of separating the polar and non-polar atom. Cs vapor was filled in cylindrical capacitor. Our experiment shows that Cs is polar atom because its capacitance is related to temperature. In the past, to realize the phase transition, ultralow temperature is necessary. But now we don’t require ultralow temperature, because we use the critical voltage Vc to achieve the phase transition. From the entropy S=Nk ln 2πe /a=0, a=dV/kTH =2πe, Vc ≈ 63volts. When V 0; when V >Vc, S < 0, phase transition occurred. When V=350 volts, the capacitance decreased from C=1.97C0 to C ≈ C0 (C0 is the vacuum capacitance), this result implies that almost all Cs atoms (more than 98.9%), like as dipoles, are aligned with the field. We create BEC with 1.928×1017 atoms, these atoms have the same momentum. Cs material with purity 99.95% was supplied by Strem Chemicals Co., USA. Both BEC and superconductivity are condensed in the momentum space, therefore these two kinds of condensation can’t be observed with the naked eye. When superconductivity occurs, the resistance R≈0, a simple and direct method to observe superconductivity is to measure the resistance by voltammetry. Similarly, when BEC occurs, the electric susceptibility χe=C/C0 –1 ≈ 0, a simple and direct method to observe BEC is to measure the capacitance by cylindrical capacitor. BEC is also a quasi-superconducting state.
Bose–Einstein condensation (BEC) at normal temperature (T=343K) has been observed because an electric field was first applied. There are two ways to achieve phase transition: lower the temperature of Bose gas or increase its density. This article provides more appropriate method: increase the voltage. In theory, 3s and 3p states of sodium are not degenerate, but Na may be polar atom doesnot conflict with quantum mechanics because it is hydrogen-like atom. Our innovation lies in we applied an electric field used for the orientation polarization. Na vapor was filled in a cylindrical capacitor. In order to determine the polarity of sodium, we measured the capacitance at different temperatures. If Na is non-polar atom, its capacitance should be independent of temperature because the nucleus of atom is located at the center of the electron cloud. But our experiment shows that its capacitance is related to temperature, so Na is polar atom. In order to achieve Na vapor phase transition, we measured the capacitance at different voltages. From the entropy of Na vapor S=0, the critical voltage Vc=68volts. When V<Vc, many atoms are in random orientation S>0; when V>Vc, the atoms become aligned with the field S<0, phase transition occurred. When V=390 volts »Vc, the capacitance decreased from C=1.9C0 to C≈C0 (C0 is the vacuum capacitance), this result implies that almost all the Na atoms (more than 98%) are aligned with the field, Na vapor entered quasi-vacuum state. We create a BEC with 2.506×1017 atoms, condensate fraction reached 98.9%. This is BEC in momentum space. Our experiment shows that if a Bose gas enters quasi-vacuum state, this also means that it underwent phase transition and generates BEC. Therefore, quasi-vacuum state of alkali gas is essentially large-scale BEC. This is an unexpected discovery. BEC and vacuum theory are two unrelated research areas, but now they are closely linked together. The maximum induced dipole moment dind≤7.8×10−15 e cm can be neglected. Ultra-low temperature is in order to make Bose gas phase transition, we achieve the phase transition by the critical voltage, so the ultra-low temperature is not necessary. According to the standard proposed by Ketterle, although we didn’t use laser cooling atoms, our experiment is real ideal BEC. Na material with purity 99.95% was supplied by Strem Chemicals Co., USA. Our experiments are easily repeated because low temperature is not necessary.
Using magnetically trapped atomic hydrogen as an example, we investigate the prospects of achieving Bose–Einstein condensation in a dilute Bose gas. We show that, if the gas is quenched sufficiently far into the critical region of the phase transition, the typical time scale for the nucleation of the condensate density is short and of O(ħ/k B T c ). As a result we find that thermalizing elastic collisions act as a bottleneck for the formation of the condensate. In the case of doubly polarized atomic hydrogen these occur much more frequently than the inelastic collisions leading to decay and we are led to the conclusion that Bose–Einstein condensation can indeed be achieved within the lifetime of the gas. Introduction In the last few years it has been clearly demonstrated that not only charged ions but also neutral atoms can be conveniently trapped and cooled by means of electro-magnetic fields. Although the physics of the various ingenious scenarios developed to accomplish this is already interesting in itself [1], the opportunities offered by an atomic gas sample at very low temperatures are exciting in their own right. Examples in this respect are the performance of high-precision spectroscopy, the search for a violation of CP invariance by measuring the electric dipole moment of atomic cesium [2], the construction of an improved time standard based on an atomic fountain [3] and the achievement of Bose–Einstein condensation in a weakly interacting gas.
We study necessary conditions for the observation of Bose–Einstein condensation in a magnetically trapped sample of atomic cesium gas. These constraints are due to interatomic collisions in the sample. We show that the prospects for observing Bose–Einstein condensation are favorable for a gas of ground-state Cs atoms in the highest state of the lowest hyperfine manifold. An interesting aspect of the calculations is that the scattering length for this f = 3, m f = −3 hyperfine state shows pronounced resonance structures as a function of applied magnetic field leading to variations of two orders of magnitude. Most importantly, the scattering length can change sign near the resonances. This suggests a controllable means to change the behavior of the Bose condensate because for negative values a condensate is unstable and other (quantum-)collective effects might be observed. The origin of the resonances is understood from the bound singlet and triplet rovibrational Cs 2 states which are perturbed due to the hyperfine and Zeeman interactions. It is a long standing goal to achieve quantum-collective effects in atomic Fermi- or Bose gases. The prominent reasons are that for a relatively simple system with low density, a microscopic theoretical treatment of the phase transition is still feasible, and to have an experimental testing ground for more complicated quantum-coherent effects such as superfluidity in 4 He and superconductivity in metals. Here, we focus on atomic species which behave as (composite) bosons.
Bose-Einstein condensation (BEC) in ultra-cold magnetically-trapped sp7Li vapor was experimentally observed and quantitative measurements of condensate number were made. Compared to other BEC experiments, lithium is unique due to its negative s-wave scattering length, corresponding to effectively attractive interactions. Due to this attraction, condensates are expected to undergo mechanical collapse if the condensate number exceeds a critical value. In this experiment, an upper limit of about 1000 condensate atoms is found, in agreement with theoretical predictions.\nIn the experiment, the atoms are confined by a set of six permanent magnets in the Ioffe configuration. Optical forces are used to slow and guide atoms from a thermal atomic beam into the magnetic trap. With about 10sp8 atoms loaded into the trap, the vapor is laser-cooled to near 200 muK and then evaporatively cooled by application of a resonantly-tuned microwave field. Evaporative cooling produces a million-fold increase in phase-space density, reaching quantum-degenerate conditions with about 10sp5 atoms at temperatures near 300 muK. After cooling, the trapped atom distribution is observed by in situ imaging via an optical probe. Calculated atom distributions are fit to the image data.\nIn initial data, the imaging resolution was insufficient to see the spatially-narrow condensate peak, but as phase-space densities approached the expected phase transition, the images suddenly became distorted. Initial fits to the data suggested as many as 10sp5 condensate atoms, in strong disagreement with theoretical predictions. An imaging model, accounting for imperfections in the imaging optics, shows that the sudden appearance of the distortions is a consequence of BEC, and that these distortions led to the initial over-estimation of cloud phase-space density and condensate number.\nImproved imaging was obtained using large probe detunings, a Phase-Contrast Polarization Imaging (PCPI) technique, and near-diffraction-limited imaging optics. The PCPI method exploits the birefringence of the trapped atoms. From the resulting images, quantitative estimates of condensate number are obtained and compared with theory.
In 1925, Einstein predicted the condensation of bosons into the ground state of the system for low (but finite) temperatures. Several phenomena, including superfluidity and superconductivity have been associated with Bose-Einstein condensation, but these systems interact strongly with their environment and pure Bose-Einstein condensation could not be established. It took 70 years, in which time the laser was discovered, and laser cooling techniques to manipulate atoms in a dilute atomic gas, before Bose-Einstein condensation in dilute atomic gases could be demonstrated in 1995. In the first condensation experiments, BECs were created in a magnetic trap. Since in a magnetic trap not all mF states of the atom can be trapped simultaneously, thereby limiting the number of experiments that can be done, other ways of trapping and generating BECs were sought and found. In 2001, the first all-optical BEC was made, where the dipole force was used to trap atoms in the crossing of two far red detuned laser beams. In an optical dipole trap not only atoms in different internal states can be trapped, but also different atomic species simultaneously. In this thesis, the formation of an all-optical Bose-Einstein condensate with rubidium atoms is presented. Conventional all-optical BECs are usually created in high power CO2 laser dipole traps, or have complicated laser cooling schemes and complex dipole trap setups. In our simple and straightforward setup, we load rubidium atoms from a magneto-optical trap into a crossed optical dipole trap created by a single frequency Yb:YAG laser with a wavelength at 1030 nm. The small wavelength allows for a small diffraction limit, and permits us to use standard optical materials, thus making the experimental setup cost effective. Other attempts to achieve Bose-Einstein condensation in a multi-mode (frequency) fiber laser at 1064 nm failed, because the atom loss was quite high. It is assumed that the multi-mode character of the fiber laser induces Raman transitions in rubidium atoms, thereby heating them. We can trap about ∼ 5E7 atoms in a single beam dipole trap out of ∼ 5E9 atoms trapped in theMOT, and ∼ 350,000 atoms can be trapped in a crossed beam dipole trap due to the smaller trap volume. 70% of the atoms in the dipole trap is optically pumped into one mF state. Quantum degeneracy is reached by evaporatively cooling the atoms in the crossed dipole trap by ramping down the laser power with three linear ramps. We can independently change the power of each beam by an AOM. This allows us to use one beam as an atom waveguide for future experiments. After evaporation, we typically have about 10,000 atoms at a temperature below the critical temperature. We have proved Bose-Einstein condensation by using the anisotropic expansion of a quantum degenerate gas trapped in an anisotropic potential. The aspect ratio of our atom cloud changed during a time of flight from 0.7 to 1.2 in 10 ms, thus proving that we have reached quantum degeneracy. We have about 5,000 condensed atoms in our optical dipole trap at a temperature less than 100 nK. The remaining atoms are thermal. Bose-Einstein condensation is obtained within 8 s, and we can repeat the experiment every 30 s. It should be mentioned that the Bose-Einstein experiment was moved from the ”Leibniz Universität Hannover” to the ”Technische Universität Darmstadt”, and had to be completely rebuilt. All-optical Bose-Einstein condensation was reached within one year after the move. Our Bose-Einstein condensation setup presents an ideal starting point for using our condensates in combination with miniaturized atom optical setups based on our novel microfabricated optical elements. With our microlenses, we can create a number of possible dipole trap configurations, such as the dipole trap array or the cylindrical microlens array. Using microlenses in miniaturized atom optical setups opens a completely new field of coherent atom optics. Also because the tight confinement of the microtraps allows us to load a 3D BEC, a 1D BEC, or a Tonks-Girardeau gas in the micropotentials depending on the density.